Simulation of convective transport during frequency chirping of a TAE using the MEGA code

We present a procedure to examine energetic particle phase-space during long range frequency chirping phenomena in tokamak plasmas. To apply the proposed method, we have performed self-consistent simulations using the MEGA code and analyzed the simulation data. We demonstrate a travelling wave in phase-space and that there exist specific slices of phase-space on which the resonant particles lie throughout the wave evolution. For non-linear evolution of an n=6 toroidicity-induced Alfven eigenmode (TAE), our results reveal the formation of coherent phase-space structures (holes/clumps) after coarse-graining of the distribution function. These structures cause a convective transport in phase-space which implies a radial drift of the resonant particles. We also demonstrate that the rate of frequency chirping increases with the TAE damping rate. Our observations of the TAE behaviour and the corresponding phase-space dynamics are consistent with the Berk-Breizman (BB) theory.

Effect of Impurity Adsorption on the Electronic and Transport Properties of Graphene Nanogaps

Graphene stands out as a versatile material with several uses in fields that range from electronics to biology. In particular, graphene has been proposed as an electrode in molecular electronics devices that are expected to be more stable and reproducible than typical ones based on metallic electrodes. In this work, we study by means of first principles, simulations and a tight-binding model the electronic and transport properties of graphene nanogaps with straight edges and different passivating atoms: Hydrogen or elements of the second row of the periodic table (boron, carbon, nitrogen, oxygen, and fluoride). We use the tight-binding model to reproduce the main ab-initio results and elucidate the physics behind the transport properties. We observe clear patterns that emerge in the conductance and the current as one moves from boron to fluoride. In particular, we find that the conductance decreases and the tunneling decaying factor increases from the former to the latter. We explain these trends in terms of the size of the atom and its onsite energy. We also find a similar pattern for the current, which is ohmic and smooth in general. However, when the size of the simulation cell is the smallest one along the direction perpendicular to the transport direction, we obtain highly non-linear behavior with negative differential resistance. This interesting and surprising behavior can be explained by taking into account the presence of Fano resonances and other interference effects, which emerge due to couplings to side atoms at the edges and other couplings across the gap. Such features enter the bias window as the bias increases and strongly affect the current, giving rise to the non-linear evolution. As a whole, these results can be used as a template to understand the transport properties of straight graphene nanogaps and similar systems and distinguish the presence of different elements in the junction.

Hubble-induced phase transitions on the lattice with applications to Ricci reheating

Using 3+1 classical lattice simulations, we follow the symmetry breaking pattern and subsequent non-linear evolution of a spectator field non-minimally coupled to gravity when the post-inflationary dynamics is given in terms of a stiff equation-of-state parameter. We find that the gradient energy density immediately after the transition represents a non-negligible fraction of the total energy budget, steadily growing to equal the kinetic counterpart. This behaviour is reflected on the evolution of the associated equation-of-state parameter, which approaches a universal value 1/3, independently of the shape of non-linear interactions. Combined with kination, this observation allows for the generic onset of radiation domination for arbitrary self-interacting potentials, significantly extending previous results in the literature. The produced spectrum at that time is, however, non-thermal, precluding the naive extraction of thermodynamical quantities like temperature. Potential identifications of the spectator field with the Standard Model Higgs are also discussed.

A Short Review on Clustering Dark Energy

We review dark energy models that can present non-negligible fluctuations on scales smaller than Hubble radius. Both linear and nonlinear evolutions of dark energy fluctuations are discussed. The linear evolution has a well-established framework, based on linear perturbation theory in General Relativity, and is well studied and implemented in numerical codes. We highlight the main results from linear theory to explain how dark energy perturbations become important on the scales of interest for structure formation. Next, we review some attempts to understand the impact of clustering dark energy models in the nonlinear regime, usually based on generalizations of the Spherical Collapse Model. We critically discuss the proposed generalizations of the Spherical Collapse Model that can treat clustering dark energy models and their shortcomings. Proposed implementations of clustering dark energy models in halo mass functions are reviewed. We also discuss some recent numerical simulations capable of treating dark energy fluctuations. Finally, we summarize the observational predictions based on these models.

Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields

We present non-perturbative numerical relativity simulations of slowly contracting spacetimes in which the scalar field driving slow contraction is coupled to a second scalar field through an exponential non-linear σ model-type kinetic interaction. These models are important because they can generate a nearly scale-invariant spectrum of super-Hubble density fluctuations fully consistent with cosmic microwave background observations. We show that the non-linear evolution rapidly approaches a homogeneous, isotropic and flat Friedmann-Robertson-Walker (FRW) geometry for a wide range of inhomogeneous and anisotropic initial conditions. Ultimately, we find, the kinetic coupling causes the evolution to deflect away from flat FRW and towards a novel Kasner-like stationary point, but in general this occurs on time scales that are too long to be observationally relevant.

Uniform convergence of operator semigroups without time regularity

When we are interested in the long-term behaviour of solutions to linear evolution equations, a large variety of techniques from the theory of $$C_0$$ C 0 -semigroups is at our disposal. However, if we consider for instance parabolic equations with unbounded coefficients on $${\mathbb {R}}^d$$ R d , the solution semigroup will not be strongly continuous, in general. For such semigroups many tools that can be used to investigate the asymptotic behaviour of $$C_0$$ C 0 -semigroups are not available anymore and, hence, much less is known about their long-time behaviour. Motivated by this observation, we prove new characterisations of the operator norm convergence of general semigroup representations—without any time regularity assumptions—by adapting the concept of the “semigroup at infinity”, recently introduced by M. Haase and the second named author. Besides its independence of time regularity, our approach also allows us to treat the discrete-time case (i.e. powers of a single operator) and even more abstract semigroup representations within the same unified setting. As an application of our results, we prove a convergence theorem for solutions to systems of parabolic equations with the aforementioned properties.

Improving the Four-Dimensional Incremental Analysis Update (4DIAU) with the HWRF 4DEnVar Data Assimilation System for Rapidly Evolving Hurricane Prediction

Short-term spin-up for strong storms is a known difficulty for the operational Hurricane Weather Research and Forecasting (HWRF) model after assimilating high-resolution inner-core observations. Our previous study associated this short-term intensity prediction issue with the incompatibility between the HWRF model and the data assimilation (DA) analysis. While improving physics and resolution of the model was found helpful, this study focuses on further improving the intensity predictions through the four-dimensional incremental analysis update (4DIAU).In the traditional 4DIAU, increments are pre-determined by subtracting background forecasts from analyses. Such pre-determined increments implicitly require linear evolution assumption during the update, which are hardly valid for rapid-evolving hurricanes. To confirm the hypothesis, a corresponding 4D analysis nudging (4DAN) method which uses online increments is first compared with the 4DIAU in an oscillation model. Then, variants of 4DIAU are proposed to improve its application for nonlinear systems. Next, 4DIAU, 4DAN and their proposed improvements are implemented into the HWRF 4DEnVar DA system and are investigated with hurricane Patricia (2015).Results from both oscillation model and HWRF model show that: 1. the pre-determined increments in 4DIAU can be detrimental when there are discrepancies between the updated and background forecasts during a nonlinear evolution. 2. 4DAN can improve the performance of incremental update upon 4DIAU, but its improvements are limited by the over-filtering. 3. Relocating initial background before the incremental update can improve the corresponding traditional methods. 4. the feature-relative 4DIAU method improves the incremental update the most and produces the best track and intensity predictions for Patricia among all experiments.

Some New Solutions of Non Linear Evolution Equations With Mutable Coefficients

We construct the traveling wave solutions of some NonLinear Evolution Equations (NLEEs) with mutable coefficients arising in different branches of physics and mathematics. we apply a novel (G′G)-formalism to construct more general solitary traveling wave solutions of NLEEs such as Sharma-Tasso-Olver with mutable coefficients and Zakharov Kuznetsov equation. Interesting solutions of NLEEs are investigated by traveling wave solutions which are in form of trigonometric, rational, and hyperbolic functions. This may build more unified new solutions for different kinds of such NLEEs with mutable coefficients arising in mathematics and physics. Wolfram Mathematica 11 is used to perform the computation work and their corresponding plots and counter graphs are plotted. This method is found to be more useful and efficient for searching the exact solutions of NLEEs.

A non-linear discrete-time dynamical system related to epidemic SISI model

We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.

Global nonexistence and blow-up results for a quasi-linear evolution equation with variable-exponent nonlinearities

"In this paper, we consider a class of quasi-linear parabolic equations with variable exponents, $$a\left( x,t\right) u_{t}-\Delta _{m\left( .\right) }u=f_{p\left( .\right)}\left( u\right)$$ in which $f_{p\left( .\right)}\left( u\right)$ the source term, $a(x,t)>0$ is a nonnegative function, and the exponents of nonlinearity $m(x)$, $p(x)$ are given measurable functions. Under suitable conditions on the given data, a finite-time blow-up result of the solution is shown if the initial datum possesses suitable positive energy, and in this case, we precise estimate for the lifespan $T^{\ast }$ of the solution. A blow-up of the solution with negative initial energy is also established."